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The conjecture that Bochner–Riesz means of the Fourier transform are bounded on L^p for the conjectured exponent range (p > 2d/(d+2) and its dual), equivalent to boundedness of the disc multiplier. Claims about its truth, partial results, and implications from or to it belong here.

The local smoothing conjecture for the wave equation implies the Bochner–Riesz conjecture.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Harmonic analysis Local smoothing conjectureimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The Bochner–Riesz conjecture implies the Fourier restriction conjecture.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Fourier restriction conjecture Harmonic analysisimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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